Heat transfer in a long, hollow cylinder which is maintained at unifor...
Ambient temperature is uniform on the periphery of cylinder and temperature is uniform. So it takes place in the radial direction only.
Heat transfer in a long, hollow cylinder which is maintained at unifor...
Direction of Heat Transfer in a Long, Hollow Cylinder with Different Temperatures on Inner and Outer Surfaces
Introduction:
When a long, hollow cylinder is maintained at uniform but different temperatures on its inner and outer surfaces, heat transfer occurs within the cylinder. Understanding the direction of heat transfer is important in various engineering applications, such as in the design of heat exchangers and thermal insulation.
Explanation:
The direction of heat transfer in this scenario can be determined by considering the temperature gradient and the thermal conductivity of the material.
Radial Heat Transfer:
In this case, heat transfer primarily occurs in the radial direction, from the inner surface to the outer surface or vice versa. This is because the temperature difference between the inner and outer surfaces creates a temperature gradient across the thickness of the cylinder. The thermal energy flows perpendicular to the surfaces, following the path of least resistance.
Temperature Gradient:
The temperature gradient is the rate at which the temperature changes per unit length. In a long, hollow cylinder, the temperature gradient is highest along the radial direction, as the temperature changes most rapidly across the thickness of the cylinder.
Thermal Conductivity:
Thermal conductivity is a material property that determines how well a material conducts heat. It quantifies the ability of a material to transfer thermal energy. In this case, the thermal conductivity of the cylinder material plays a significant role in determining the direction of heat transfer.
Key Points:
- Heat transfer occurs primarily in the radial direction in a long, hollow cylinder with different temperatures on its inner and outer surfaces.
- The temperature gradient across the thickness of the cylinder is highest along the radial direction.
- The thermal conductivity of the cylinder material influences the rate of heat transfer.
Conclusion:
In summary, heat transfer in a long, hollow cylinder with different temperatures on its inner and outer surfaces primarily occurs in the radial direction. The temperature gradient across the thickness of the cylinder is highest along the radial direction, and the thermal conductivity of the cylinder material determines the rate of heat transfer.